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Let f: R to R be a continous function. ...

Let `f: R to R` be a continous function.
Let `theta_(n) = pi int_(1//n)^(n) f(x + 1/x) (log x)/x dx, n =1,2`,…….. Then `cos^(-1) [sum_(k=1)^(22) 1/k sin theta_(k)]`=…………………

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Knowledge Check

  • Let f be a positive function. Let I_(1) int_(1-k)^(k) x.f {x(1-x)} dx, I_(2)= int_(1-k)^(k) f{x(1-x)}dx where 2k-1 gt 0 , then I_(1)//I_(2) is

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